# What is a Mean Return?

A portfolio of investments faces risks that could affect the actual return earned by the investor. No method exists to accurately calculate the actual return, but mean return takes into account the risks that face a portfolio and calculates the rate of return the investor can expect to get from that particular portfolio. Investors can use the concept to calculate the expected return of securities, and firm managers can use it in capital budgeting when deciding whether to take on a certain project.

In capital budgeting, this type of calculation considers several possible scenarios and the probability of each scenario happening; it then uses these figures to determine the likely worth of a project. For example, a project has a 25 percent probability of generating $1,200,000 US Dollars (USD) under good circumstances, a 50 percent probability of generating $1,000,000 USD under normal circumstances and a 25 percent probability of generating $800,000 USD under bad circumstances. The project's mean return is then = (25% X $1,200,000 USD) + (50% X $1,000,000 USD) + (25% X $800,000 USD) = $1,000,000 USD.

In securities analysis, mean return can apply to a security or a portfolio of securities. Each security in a portfolio has an average return calculated using a formula similar to the one for capital budgeting, and the portfolio also has such a return that predicts the average expected value of all the likely returns of its securities. For example, an investor has a portfolio consisting of 30 percent of Stock A, 50 percent of Stock B and 20 percent of Stock C. The mean return of Stock A, Stock B and Stock C are 10 percent, 20 percent and 30 percent, respectively. The mean return of the portfolio can then be calculated to be = (30% X 10%) + (50% X 20%) + (20% X 30%) = 19 percent.

This type of calculation can also show average return over a certain period of time. To make this calculation, there has to be data over a few periods of time, with a higher number of periods generating more accurate results. For example, if a firm earns a return of 12 percent in Year 1, -8 percent in Year 2 and 15 percent in Year 3, then it has an annual arithmetic mean return of = (12% - 8% + 15%) / 3 = 6.33%.

Geometric mean return also calculates proportional change in wealth over a particular period of time. The difference is that this calculation shows the rate of wealth growth if it grows at a constant rate. Using the same figures as the previous example, the annual geometric mean return is calculated to be = [(1 + 12%) (1 - 8%) (1 + 15%)]^{1/3} - 1 = 5.82%. This figure is lower than the arithmetic average return, because it takes into account the compounding effect when interest is applied on an investment that has already earned interest during the previous period.

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